 | Hastings Berkeley - 1910 - 279 Seiten
...— Suggestion that they are real Axioms of Direction. EUCLID'S Axiom of Parallels runs as follows : If a straight line meet two straight lines, so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles. The reason which made... | |
 | James Byrnie Shaw - 1918 - 222 Seiten
...approach also, that is, in non-Euclidean geometry. Euclid had among his postulates one which read thus : If a straight line meet two straight lines so as to...lines, being continually produced, shall at length meet upon that side of the line on which are the angles which are less than two right angles. For ages mathematicians... | |
 | Robert T. Browne - 1919 - 426 Seiten
...mankind. The parallel-postulate, as stated by EUCLID in his Elements of Geometry, reads as follows: "If a straight line meet two straight lines so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." On this postulate hang... | |
 | Charles Austin Hobbs - 1921 - 216 Seiten
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular... | |
 | 1901 - 488 Seiten
...far from "self-evident" it is the reader may judge for himself. "If a straight line meets two other straight lines so as to make the two interior angles...it taken together less than two right angles, these sides being continually produced shall at length meet on that side on which are the angles which are... | |
 | John Whitehead, L. F. Whitehead - 1928 - 514 Seiten
...part. I0. Two straight lines cannot enclose a space Ii. AU right angles are equal to one another. I2. If a straight line meet two straight lines, so as...it taken together less than two right angles, these two straight lines being continually produced shall at length meet on that side on which are tht angles... | |
 | Franklin D. Jones - 1928 - 1254 Seiten
...a space, n. All right angles are equal to one another. 12. If a straight line intersects two other straight lines, so as to make the two interior angles...side of it taken together less than two right angles, then these straight lines, if continually produced, must meet upon the side on which the angles are... | |
 | 1886 - 548 Seiten
...of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is: — "If a straight line meets two straight lines, so as to make the two interior...lines being continually produced shall at length meet upon that side on which are the angles which are less than two right angles." In other words, if the... | |
 | Roberto Bonola - 1955 - 452 Seiten
...parallels cut hy a transversal make equal alternate angles, he hrings m the unwieldly postulate or axiom: " If a straight line meet two straight lines, so as...less than two right angles, these straight lines, heing continually produced, shall at length meet on that side on which are the angles which are less... | |
 | Ivor Grattan-Guinness, Gerard Bornet - 1997 - 310 Seiten
...4. And that all right angles are equal to one another. 5. And that if a straight line meet two other straight lines so as to make the two interior angles...these straight lines being continually produced shall meet on that side on which are the angles which are less than two right angles. 6. And that two straight... | |
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If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles... 
